Question: Simplify the following expression: $ r = \dfrac{2z - 8}{z - 10} + \dfrac{-2}{9} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{2z - 8}{z - 10} \times \dfrac{9}{9} = \dfrac{18z - 72}{9z - 90} $ Multiply the second expression by $\dfrac{z - 10}{z - 10}$ $ \dfrac{-2}{9} \times \dfrac{z - 10}{z - 10} = \dfrac{-2z + 20}{9z - 90} $ Therefore $ r = \dfrac{18z - 72}{9z - 90} + \dfrac{-2z + 20}{9z - 90} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{18z - 72 - 2z + 20}{9z - 90} $ $r = \dfrac{16z - 52}{9z - 90}$